Angular Velocity Problem - Merry Go Round

A 4.8m diameter merry-go-round is rotating freely with an angular velocity of 0.8rad/s. Its total moment of inertia is 1950(kg)(m2). Skid, Mitch, Larry, and Greezy all jump on at the same time. They each have a mass of 65kg.What is the angular velocity now?

This is not actually correct. 1/2 mv^2 is the formula for kinetic energy. The moment of inertia of a rotating body is something totally different, and it depends on both the mass of the body and its shape. But you don't have to worry about how to calculate it, because the problem *gives* you its numerical value right from the start.

Right, and the quantity that changes (before vs. after) is the moment of inertia of the merry go round, because now it has the additional individual moments of inertia of the people standing on it. If you can figure out by how much I changes, you can figure out how much omega changes (because angular momentum is conserved).